Orthogonal frequency division multiplexing (OFDM) provides an effective approach to combat multipath with high bandwidth efficiency for underwater acoustic communication, thus design and implementation of acoustic OFDM MODEMs draw more and more attention. Extensive work has been performed to mitigate multipath, Doppler shift, and peak average power ratio from the viewpoint of theoretical analysis. Meanwhile, design and implementation of a parameter-configurable OFDM to adapt to highly diverse underwater channels and various missions become more and more important. Traditional MODEM with fixed parameters cannot achieve the best tradeoff between data rate and bit error rate. In order to obtain the best communication performance under long time delay channels, Doppler channels, and frequency-selective channels, in this paper, we provide the design and implementation of a parameter-configurable underwater acoustic OFDM MODEM with the purpose to achieve flexibility. Specifically, the reconfigurable parameters of the OFDM MODEM include the number of receivers, the number of null subcarriers, the number of pilot subcarriers, as well as the type of channel estimation algorithms. The number of pilot subcarriers and type of channel estimation methods are determined based on channel characteristics, the number of null subcarriers is determined based on the Doppler shift, and the number of the received channels is based on fading channel. Moreover, in this paper, the Doppler estimation performance under different number of null subcarriers, and the channel estimation performance under different number of pilot subcarriers and under different channel estimation algorithms, are analyzed in terms of bit error rate. Finally, the effectiveness of the proposed highly configurable OFDM MODEM is demonstrated by two sea trials corresponding to different communication scenarios.